From Police Comics #17, published in 1943.
Plastic Man and Woozy are chasing a murderer in a cooky mansion. The killer traps Plastic Man's head in a vaccuum cleaner and puts it in reverse. Plastic Man's inherent stretching power allows him to inflate to a massive size by the time Woozy catches up with him. (The next page has Woozy and Plastic Man rescued by a stranger in the dark. No further inflation scenes are shown.)
As a reader of the Plastic Man comics that proceeded this one, I think I can say this is the first time Plastic Man was inflated.
